Optimal sampling of water distribution network dynamics using graph Fourier transform

Water distribution networks are critical infrastructures under threat from the accidental or intentional release of contaminants. Data collection sensors remains challenging in underground spaces and large networks. In order to quantify the threat of contamination to end users, inferring contaminant spread with minimal sensor data is critical. Existing sensor deployment optimisation approaches use numerical optimisation, but suffer from scalability issues and lack performance guarantees. Analytical graph theoretic approaches link complex network topology (e.g. Laplacian spectra) to optimal sensing locations, but neglects the complex fluid dynamics. Alternative data-driven approaches such as compressed sensing offer limited sample node reduction. In this work, we introduce a novel data-driven Graph Fourier Transform that exploits the low-rank property to optimally sample WDNs. The proposed GFT allows us to recover the full dynamics of network contamination using only data sampled at a subset of nodes. It offers attractive improvements over existing numerical, compressed sensing, and graph theoretic approaches. Our case study results show that, on average, with nearly 30% of the junctions monitored, we are able to fully recover the networked dynamics. The framework is useful beyond the application of WDNs and can be applied to a variety of infrastructure sensing for digital twin modeling.